The expressive power of memory logics

Abstract. We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic HL(↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain. This work focuses in the case where the memory is a set, and we can test whether the current node belongs to the set or not. We prove that, in terms of expressive power, the memory logics we discuss here lie between the basic modal logic K and HL(↓). We show that the satisfiability problem of most of the logics we cover is undecidable. The only logic with a decidable satisfiability problem is obtained by imposing strong constraints on which elements can be memorized. §1. Modal Logics and Memory Logics Nowadays, the term modal logics loosely refers to an extremely wide variety of languages, which are used in many different applications (see, e.g., (Blackburn et al., 2006)). Actually, the fact that the number of members in this family keeps constantly increasing is one of the definin